GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
59 views

asked in Algorithms by Active (2.3k points)   | 59 views
Answer should be D.

2 Answers

+3 votes
Best answer

mit quiz pdf link. here is the required part:

answered by Veteran (43.9k points)  
selected by
+3 votes
$f(n) = \Theta(g(n))$ and $g(n) = \Theta(h(n))$ implies $f(n) = \Theta(h(n))$ (by transitivity).

Now $f(n) = \Theta(h(n))$ implies $h(n) = \Theta(f(n))$ (symmetry property). So statement I is true.

Similarly in statement II, by transitivity, we get $f(n) = O(h(n))$ this implies $h(n) = \Omega(f(n))$, by transpose symmetry.

Statement III is false.  consider  $f(n) = n^2$ and $g(n)=4n^2$

Statement III would be true, if the conclusion was $f(n) = \Theta(g(n))$ or $g(n) = \Theta(f(n))$.

You can refer to these properties in CLRS.
answered by Loyal (3.3k points)  

Related questions

+2 votes
0 answers
2
asked in Algorithms by Null&Void Active (1.8k points)   | 62 views


Top Users Mar 2017
  1. rude

    5118 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2730 Points

  5. Debashish Deka

    2602 Points

  6. 2018

    1574 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1382 Points

  9. Bikram

    1350 Points

  10. Sanjay Sharma

    1128 Points

Monthly Topper: Rs. 500 gift card

21,531 questions
26,861 answers
61,191 comments
23,207 users